Introduction to Computer Algebra

Articles and project topics
 

• The transposition principle:
   
  • Bostan, A., Lecerf, G., and Schost, É. (2003, August). Tellegen's principle into practice. In Proceedings of the 2003 international symposium on Symbolic and algebraic computation (pp. 37-44). ACM.
  • Kaltofen, E. (2000). Challenges of symbolic computation: my favorite open problems. Journal of Symbolic Computation, 29(6), 891-919.
  • Kedlaya, K. S., and Umans, C. (2011). Fast polynomial factorization and modular composition. SIAM Journal on Computing, 40(6), 1767-1802.
  
   
• Sparse polynomial interpolation:
   
  • Kaltofen, E., and Lee, W. S. (2003). Early termination in sparse interpolation algorithms. Journal of Symbolic Computation, 36(3), 365-400.
  • Giesbrecht, M., Labahn, G., and Lee, W. S. (2006, July). Symbolic-numeric sparse interpolation of multivariate polynomials. In Proceedings of the 2006 international symposium on Symbolic and algebraic computation (pp. 116-123). ACM.
  • Garg, S., and Schost, É. (2009). Interpolation of polynomials given by straight-line programs. Theoretical Computer Science, 410(27), 2659-2662.
  
   
• Discovering integer relations:
   
  • The LLL Algorithm: Survey and Applications. Phong Q. Nguyen, and Brigitte Vallée, Eds. Springer Science < Business Media, 2009.
  • Chen, J., D. Stehlé, and Villard, G. (2013). A new view on HJLS and PSLQ: sums and projections of lattices. ISSAC'13, Boston, USA, 2013. ACM.
  • Håstad, B. Just, Lagarias, J., and Schnorr, C (1989). Polynomial time algorithms for finding integer relations among real numbers. SIAM J. Comput., 18(5):859-881.